Question

22. The means of samples of sizes 50 and 75 are 60 and x respectively. If the
mean
of the combined group is 54 ; find x​

Answer 1

Step-by-step explanation:

Given:-

The means of samples of sizes 50 and 75 are 60 and x respectively. And the mean of the combined group is 54 .

To find:-

Find x?

Solution:-

The mean of samples of sizes 50 = 60

The total samples of sizes 50

=> 50×60

=> 3000

The mean of samples of sizes 75 = X

The total samples of sizes 75

=> 75×X

=> 75X

Total number of both samples of both sizes

=> 3000+75X

Total sizes of both samples

= 50+75

= 125

We know that

Mean = Sum of all observations/Number of all observations

=> Mean = (3000+75X)/125

According to the given problem

Mean of the combined group = 54

=> (3000+75X)/125 = 54

=> 3000+75X = 54×125

=> 3000+75X = 6750

=>75X = 6750-3000

=> 75X = 3750

=> X = 3750/75

=> X = 50

Alternative Method:-

Combined Mean = (f1x1+f1x2+...+fnxn)/(f1+f2+...+fn)

=> [(50×60)+(75×X)]/(50+75) = 54

=> (3000+75X)/125 = 54

=>3000+75X = 54×125

=> 3000+75X = 6750

=> 75X = 6750-3000

=>75X = 3750

=>X = 3750/75

=> X = 50

Answer:-

The value of X for the given problem is 50

Used formulae:-

• Mean = Sum of all observations/Number of all observations